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<div class="titlepage"><div><div><h3 class="title">
<a name="boost_numeric_odeint.concepts.second_order_system"></a><a class="link" href="second_order_system.html" title="Second Order System">Second
      Order System</a>
</h3></div></div></div>
<h5>
<a name="boost_numeric_odeint.concepts.second_order_system.h0"></a>
        <span class="phrase"><a name="boost_numeric_odeint.concepts.second_order_system.description"></a></span><a class="link" href="second_order_system.html#boost_numeric_odeint.concepts.second_order_system.description">Description</a>
      </h5>
<p>
        The Second Order System concept models the algorithmic implementation of
        the rhs for steppers requirering the second order derivative, hence the r.h.s.
        of the ODE <span class="emphasis"><em>x'' = f(x,x',t)</em></span>. The only requirement for
        this concept is that it should be callable with a specific parameter syntax
        (see below). A Second Order System is typically implemented as a function
        or a functor. Systems fulfilling this concept are required by the Velocity
        Verlet method.
      </p>
<h5>
<a name="boost_numeric_odeint.concepts.second_order_system.h1"></a>
        <span class="phrase"><a name="boost_numeric_odeint.concepts.second_order_system.notation"></a></span><a class="link" href="second_order_system.html#boost_numeric_odeint.concepts.second_order_system.notation">Notation</a>
      </h5>
<div class="variablelist">
<p class="title"><b></b></p>
<dl class="variablelist">
<dt><span class="term"><code class="computeroutput"><span class="identifier">System</span></code></span></dt>
<dd><p>
              A type that is a model of Second Order System
            </p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">Space</span></code></span></dt>
<dd><p>
              A type representing the state <span class="emphasis"><em>x</em></span> of the ODE
            </p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">Velocity</span></code></span></dt>
<dd><p>
              A type representing the derivative <span class="emphasis"><em>x'</em></span> of the ODE
            </p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">Acceleration</span></code></span></dt>
<dd><p>
              A type representing the second order derivative <span class="emphasis"><em>x''</em></span>
              of the ODE
            </p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">Time</span></code></span></dt>
<dd><p>
              A type representing the time
            </p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">sys</span></code></span></dt>
<dd><p>
              An object of type <code class="computeroutput"><span class="identifier">System</span></code>
            </p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">x</span></code></span></dt>
<dd><p>
              Object of type <code class="computeroutput"><span class="identifier">Space</span></code>
            </p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">v</span></code></span></dt>
<dd><p>
              Object of type <code class="computeroutput"><span class="identifier">Velocity</span></code>
            </p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">a</span></code></span></dt>
<dd><p>
              Object of type <code class="computeroutput"><span class="identifier">Acceleration</span></code>
            </p></dd>
<dt><span class="term"><code class="computeroutput"><span class="identifier">t</span></code></span></dt>
<dd><p>
              Object of type <code class="computeroutput"><span class="identifier">Time</span></code>
            </p></dd>
</dl>
</div>
<h5>
<a name="boost_numeric_odeint.concepts.second_order_system.h2"></a>
        <span class="phrase"><a name="boost_numeric_odeint.concepts.second_order_system.valid_expressions"></a></span><a class="link" href="second_order_system.html#boost_numeric_odeint.concepts.second_order_system.valid_expressions">Valid
        expressions</a>
      </h5>
<div class="informaltable"><table class="table">
<colgroup>
<col>
<col>
<col>
<col>
</colgroup>
<thead><tr>
<th>
                <p>
                  Name
                </p>
              </th>
<th>
                <p>
                  Expression
                </p>
              </th>
<th>
                <p>
                  Type
                </p>
              </th>
<th>
                <p>
                  Semantics
                </p>
              </th>
</tr></thead>
<tbody><tr>
<td>
                <p>
                  Calculate <span class="emphasis"><em>x'' := f(x,x',t)</em></span>
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput"><span class="identifier">sys</span><span class="special">(</span>
                  <span class="identifier">x</span> <span class="special">,</span>
                  <span class="identifier">v</span> <span class="special">,</span>
                  <span class="identifier">a</span> <span class="special">,</span>
                  <span class="identifier">t</span> <span class="special">)</span></code>
                </p>
              </td>
<td>
                <p>
                  <code class="computeroutput"><span class="keyword">void</span></code>
                </p>
              </td>
<td>
                <p>
                  Calculates f(x,x',t), the result is stored into a.
                </p>
              </td>
</tr></tbody>
</table></div>
</div>
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<td align="right"><div class="copyright-footer">Copyright © 2009-2015 Karsten Ahnert and Mario Mulansky<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
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